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Cellulose (2016) 23:2249–2272
Calculation of IWWS
Miettinen et al. 2009; Salminen 2010), thus determin- ing productivity. Against this background, it is critical for both scientists and practitioners to understand the effects of forces and conditions that can be influenced, leading to increased IWWS. This understanding is a prerequisite to be able to draw the correct conclusions regarding the development of new processes and additives.
Page developed a specific function for IWWS based on his equation for the tensile strength of a dry sheet by including the effects of fiber length and coarseness (Page 1969, 1993). Shallhorn enhanced this equation by considering the effect of pressing load (Shallhorn 2002). This incorporates the fiber length and coarse- ness as fiber morphology parameters, as well as the surface tension of the solvent water. Shallhorn showed that this function is limited to the large-fiber fraction of softwood kraft pulps. When using this Eq. 1, it is important to bear in mind that fines and short fibers are not considered. But those fiber fractions have a great impact on the IWWS and are widely used in papermaking. In addition, surfactants and web temperature clearly have a significant impact on the surface tension of the water and thus on the IWWS of the paper web. Calculation of IWWS (Page 1993; Shallhorn 2002). T IWWS ¼ 1 Þ T IWWS : initial wet web tensile strength; g : friction coefficient between two wet fibers; c : surface tension of water; L: fiber length; W: fiber width at moisture contents between 20 and 60 %; RBA (dry) : Relatively Bonded Area (proportion of the fiber surface contained within a water meniscus); C: fiber coarseness; t: minor axis of the elliptical cross-section of the fiber. 0 : 37 pgc LW RBA dry Ct ð Þ ð
Definition
The IWWS identifies the tensile energy absorption of a wet paper web during the production process. Gener- ally, the designation ‘‘initial wet’’ spans a dryness level from approximately 10 % during web formation up to approx. 60 % in the first dryer. Until approxi- mately 1960, research papers noted dryness levels of approximately 10 %. These values were measured downstream in the forming section or by laboratory web forming equipment. Today, depending on the construction of the forming section and the fibrous material, dryness levels of 18 % up to a maximum of 25 % are achieved. In this context, it is important to consider the different interactions among interfaces during sheet formation (Fig. 1). Solids are dispersed in water at the headbox and on the wire in stage 1. At the end of the wire and in the pressing section, the water contains both, solids and air, with the air presenting another surface interaction to be considered in stage 2. Stage 3 starts in the press section. From here on, solids and water are in air. Due to these different interfaces and the interactions among solids, water and air, the relationships among these components have a critical impact on paper strength. In accordance with ISO 3781, the wet strength of a specific paper type indicates the strength of a manu- factured paper after remoistening, not to be confused with IWWS. In addition to the IWWS, the dry strength of paper has been extensively studied. As a rule, the term ‘‘dry strength’’ indicates the strength of paper after manufacturing with a dryness level of [ 85%. The wet and dry strength of paper follow different rules and principles compared to the IWWS. This literature review considers the IWWS of paper at dryness levels from approx. 10 to 60 %. This review explains the different behaviors of fibers and additives on paper strength properties, with a focus on the IWWS.
Explanatory levels
To explain the IWWS, results from the reviewed literature is divided by scale and considered system- atically at the molecular level (nanometer range), the fiber morphology (micrometer range) and the paper level (macro range). Figure 2 emphasizes the fact that these levels of explanation overlap. This figure shows that although the individual levels are studied sepa- rately, it is important to consider that they occur concomitantly, interacting with and influencing each other. These interactions are addressed in papers referenced in the individual chapters and in the section ‘‘Integral explanatory models’’. As described in the previous paragraph, the strength properties of paper strongly depend on the dryness
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